Each airline is different. Don't check any seats at the counter. Bring them both to the gate and they wont count against your luggage allowance. This will also give you the option of bringing the younger child's car seat on board if they have an extra seat for it. Not only will you be sure to have your car seat at your destination but you and your child will have a more comfortable and safer ride. Sounds like the older child's car seat would be hard to replace anyway. Compensation wont be offered if lost or broken, which happens a lot...
Most airlines allow an extra item for lap babies, presumably, the diaper bag so no, you'll still get your own bag too. Some foreign airlines even have a baggage allowance for lap babies so check into that, if it applies.
Your older son is a full-fledged passenger so gets the full check-in and carry-on item limits as an adult would, even if the ticket is discounted (a bit, which is rare these days!)
Actually, your son's car seat might still be compliant, if you're flying a U.S. company. Did you know that the FAA makes exceptions for special needs children?
You might have to dig but it's in this FAA document;
http://www.faa.gov/documentLibrary/m...%20120-87B.pdf
You might want to "booster train" your 6 year old before leaving, if you choose to go that route. Make sure he sits in it well and doesn't wiggle out (common with lots of kids).
Some parents fit the back part of the booster in the suitcase and then bring the bottom part as a carry-on.
Your older child's stroller also might fall into the category of handicapped mobility devices, which are protected by law so look into this, if you are flying a U.S. company. It might not only be exempted but its treatment guaranteed (which isn't the case with normal car seats).
Contact whatever organization deals with your son's special needs as they might be more informed about the specific situation.
On a personal note, as many here will confirm, when you fly with multiple children and their devices, the airlines often let the odd item "slide". Don't point it out, be nice at check-in and by all means, don't ask! (because the nice agent who was about to give you a break realizes his supervisor is in earshot lol!)